Northampton substitute Colin Larkin had only been on the pitch nine minutes when he cracked home a superb equaliser.
Former England international Anderton gave his side a deserved lead in the 34th minute. Midfielder Max Gradel crossed to Lee Bradbury, who teed up Anderton to hit the ball home from 15 yards past Mark Bunn in the Town goal.
Bournemouth defender Russell Perrett tore his hamstring and was carried off in the 48th minute and was replaced by substitute Warren Cummings.
Defender Cummings then fell awkwardly after barely 12 minutes on the pitch and broke his left arm in a bad fall.
The defensive chaos cost Bournemouth as Larkin got on the end of Bradley Johnson's cross before crashing the ball home from 25 yards into the top right-hand corner.
Earlier referee Danny McDermid infuriated the Bournemouth players by waving away a stonewall penalty. Jo Kuffour went round goalkeeper Bunn and appeared to be brought crashing to the floor.
McDermid waved away the furious appeals of a penalty.
Anderton went close for Bournemouth with a free kick in the 70th minute after he had been brought down just outside the box by Mark Hughes. Anderton fired the resulting free-kick inches over the bar with Bunn well beaten.
Gradel almost forced Hughes into conceding an own goal with a wicked cross on 70 minutes, but the defender did well just to flip the ball over the bar.
Both sides had chances to win the game in injury time with Bournemouth going close through Josh Gowling and Anderton in a goalmouth scramble.
Northampton striker Andy Kirk almost snatched three points for his side when he fired a volley from 25 yards just over the bar.